Interpolation filter and method for digitally interpolating a digital signal

ABSTRACT

The invention relates to an interpolation filter and to a method for filtering a digital input signal. The interpolation filter has an amplitude characteristic with a low-pass-shaped damping curve in the useful signal frequency range of the digital input signal. The group delay time of the interpolation filter is essentially constant in the useful signal frequency range and can be adjusted within a clock period of the equidistant digital signal.

TECHNICAL FIELD

The invention relates to an interpolation filter and a method forinterpolating a digital signal that can be used, in particular, forsampling frequency conversion.

BACKGROUND ART

There are a multiplicity of applications in which it is necessary tovary the frequency of a given digital equidistant time signal by meansof digital filtering. Interpolation filters are used as componentcircuits in digital switching systems in which a change in the samplingfrequency of digital signals is necessary. Systems that are concernedonly with simple integral sampling frequency ratios are not the subjectmatter of the invention.

Methods for arbitrarily changing sampling frequencies are described in“IEEE, Transactions of Acoustics, Speech and Signal Processing”, VolumeASSP-32, No. 3, July 1984, pages 577–591 under the title of “DigitalMethods for Conversion between Arbitrary Sampling Frequencies”, author:T. A. Ramstad. The associated circuits are denoted as hybrid systemsthat consist of a first interpolation filter with a fixed samplingfrequency ratio, and a second interpolation filter. The secondinterpolation filter determines intermediate values that lie arbitrarilyin time between the fixed samples of the sampling lattice downstream ofthe second interpolation filter, and thus permit arbitrary samplingfrequency ratios. The first interpolation filter includes aninterpolation device and a digital filter as a combination. Theinterpolation device, which is also denoted as an oversampling device,is used to insert “0” values between the original samples in accordancewith an oversampling factor N. A downstream digital filter is the firstto smooth the variation in the digital samples, the signal jumps to the0 values, in particular, being compensated such that the spectrum of theuseful signal is not falsified by higher frequency components. The firstinterpolation filter is designed for this purpose such that relativelylarge frequency band gaps are formed in the infinitely extendingfrequency spectrum. It holds in the case of oversampling as well thatthe frequency spectra are reflected at half the original samplingfrequency and multiples thereof. However, a new sampling frequency thatforms an integral frequency ratio with the original sampling frequencyis to be assumed downstream of the interpolation device and of thedigital filter. The digital filter in this case removes the remainingspectral components between the useful signal band and the reflectedfrequency band in the case of the new sampling frequency and theassociated frequency multiples. The digital filter functions in thiscase simply as a digital lowpass filter that passes the useful signalfrequency band and suppresses the frequency components thereabove. Inthis case, however, a reflection occurs at half the sampling frequencyin accordance with the sampling theorem. It follows that a digitallowpass filter cannot suppress the multiples of the sampling frequency.

The spectral signal components in the new sampling frequency and thefrequency multiples must be suppressed for the implementation ofarbitrary sampling frequency ratios. If these signal interferencecomponents are not suppressed, signal interference components occur inthe useful signal frequency band during the generation of arbitrarysampling frequency ratios. The first interpolation filter is describedin “Proceedings of the IEEE”, Volume 61, No. 6, June 1973, pages692–702, and in the article by R. W. Schafer and L. R. Rabbiner entitled“A Digital Signal Processing Approach to Interpolation”.

A method having a hybrid system for sampling frequency conversion isdisclosed in EP-A-0 561 067. This system operates with an oversamplingfactor of N=2, and therefore achieves only a relatively poorsignal-to-noise ratio. This poor signal-to-noise ratio is tolerable inthe case of this hybrid system since it is used for video signalapplications. A second interpolation filter is implemented as a lowpassfilter that suppresses all signal components whose frequencies aregreater than 1.5 times the value of the original sampling frequency. Theanalog lowpass response is achieved with the aid of a transverse filterin the case of which the weighting factors of the stored samples dependon a time difference value. Such a lowpass filter suppresses in thiscase not only the remaining spectral signal components in the frequencymultiples of the new sampling frequency, but the entire frequencyspectral region above a blocking edge. Although having a comparabletransmitting/blocking characteristic, in comparison with a correspondingcomb filter arrangement such a lowpass filter can be implemented only atgreat expense.

The “Journal of Audio Engineering Society”, Volume 41, No. 7/8, 1993,pages 539–555 by R. Adams and T. Corn entitled “Theory and VLSIArchitectures for Asynchronous Sample Rate Converters” describes amethod for a sampling frequency conversion system that treats the use ofrelatively simple sample-and-hold circuits, on the one hand, and the useof lowpass filters as analog resamplers, on the other hand.

After the N-fold oversampling and filtering there are present in eachcase in the frequency spectrum downstream of the first interpolationfilter in the abovenamed systems interference signal frequency bandswhose center frequencies are at the frequency multiples of the newsampling frequency. The frequency bandwidth of each signal interferenceregion is equal in this case to double the frequency bandwidth of theuseful signal. If the Nyquist condition for the original digitization isfulfilled, the frequency bandwidth of the interference signal regionexhibits in the limiting case at most the value of the original samplingfrequency. The position and bandwidth of all the interference regionsare defined in the frequency spectrum by the original sampling frequencyand the original oversampling factor N. The N-fold oversampling of theoriginal digital sampling frequency has the effect that the relativefrequency bandwidth of the interference signal regions in the frequencyspectrum is reduced by the factor of 1/N referred to the new samplingfrequency. This facilitates the separation of the useful signalfrequency band from the respective interference signal frequency region,since the transition region between the transmission and the blockingfrequency band for the second interpolation filter is enlarged. Thisreduces the outlay on circuitry required for the second interpolationfilter. However, the price for this is a higher outlay on circuitry forthe smoothing filter in the first interpolation filter. There istherefore either a need for a very complicated first interpolationfilter and a simple second interpolation filter, for example a linearinterpolator, or there is a simple first interpolation filter, forexample with a very small oversampling, and a very complicated lowpassfilter with the aid of which the analog resampler is implemented.

SUMMARY OF THE INVENTION

EP 0 696 848 A1 therefore proposed for the purpose of digitalinterpolation of signals a method which leads to a very highsignal-to-noise ratio in conjunction with a low outlay on circuitry forthe filter system, which consists of a first and second interpolationfilter. In this method for digital interpolation of signals, weightingfactors or filter coefficients are multiplied by delayed input values ofa digital signal that has a first clock frequency, the delay dependingon a time difference value which is determined by the interpolationinstant and by the time pattern of the first clock signal. The filtercoefficients of the interpolation filter are determined by the pulseresponse h(t) in the time domain. The associated transfer function H(F)has in the frequency domain a signal attenuation characteristic which,with reference to the stop bands, is restricted essentially to thesignal interference regions situated at the frequency multiples of thefirst clock frequency. In this case, at least two mutually adjacent zeropoints are assigned to each of these signal interference regions in thefrequency band. Given the presence of zero points of double order, atleast one further zero point of the transfer function H(F) is assignedto at least one of the interference regions and the associated periodicinterference regions.

The amplitude response of the interpolation filter described in EP 0 696841 A1 varies like a comb and, because of the narrowband interferencesignal frequency bands, exhibits an only very narrowband useful signalfrequency band.

It is therefore the object of the present invention to create aninterpolation filter for filtering a digital input signal, and a methodfor digital interpolation of digital input signals that exhibit abroadband useful signal frequency band.

This object is achieved according to the invention by means of aninterpolation filter.

The invention creates an interpolation filter for filtering a digitalinput signal whose amplitude response exhibits a lowpass-typeattenuation curve in the useful signal frequency band of the digitalinput signal.

Because of the broadband useful signal frequency band, the interpolationfilter according to the invention offers the advantage that it is alsopossible to process broadband digital input signals.

A further advantage consists in that the interpolation filter accordingto the invention can also be used for analog-to-digital converters withvery high sampling frequencies since, in practical applications, theentire circuit is calculated for an only onefold to fourfold usefulsignal bandwidth.

The low sampling frequencies or the long clock periods T of the digitalsignal processing offer the advantage that the components of theinterpolation filter, for example demultiplexers, operate at lowfrequencies and can therefore be implemented with particular ease interms of circuitry.

This has the advantage, in turn, that the components of theinterpolation filter can be integrated on a small chip area and have alow power consumption.

In an advantageous refinement of the interpolation filter according tothe invention, there is connected downstream of the interpolation filtera highpass filter for compensating the lowpass-type amplitude responseof the interpolation filter.

This offers the advantage that signal distortions are removed because ofthe lowpass-type attenuation curve in the filtered output signal of theinterpolation filter.

The group delay of the interpolation filter advantageously runs in anessentially constant fashion in the useful signal frequency band of thedigital input signal.

The digital input signal that is filtered by the interpolation filteraccording to the invention is preferably an equidistant digital signalwith a predetermined clock pulse period T_(in).

In this case, the group delay of the interpolation filter according tothe invention can preferably be set inside the clock pulse period T_(in)of the digital input signal.

The ratio of the clock pulse periods of the digital input signal T_(in)and the digital output signal T_(aus) filtered by the interpolationfilter can preferably be set.

In a particularly preferred embodiment, the interpolation filter and thedownstream highpass filter together exhibit a sinc filtercharacteristic.

A further interpolation filter is preferably connected upstream of theinterpolation filter for the purpose of constricting the useful signalfrequency band.

The upstream interpolation filter is preferably a polyphase filter.

In a particularly preferred embodiment of the interpolation filteraccording to the invention, the interpolation filter consists of

a filter coefficient generator for generating filter coefficients as afunction of a base function,

a multiplier for multiplying the digital input signal by the generatedfilter coefficients, and an accumulator for accumulating the digitalinput signal weighted by the multiplication.

The base function is preferably stored in a storage device of theinterpolation filter.

As an alternative to this, in accordance with a further embodiment theinterpolation filter according to the invention has a base functiongenerator for generating the base function as a function of fundamentalfunctions.

It is preferred for this purpose to provide a storage device for storingthe fundamental functions.

In a preferred embodiment of the interpolation filter according to theinvention, the latter has a controllable switching device that can beswitched for reading out the weighted digital input signal as digitaloutput signal.

In a preferred embodiment, the accumulator consists of an adder and aregister whose output is fed back to an input of the adder.

The invention further creates a method for digital interpolation of adigital input signal.

The invention creates a method for digital interpolation of a digitalinput signal having the following steps, specifically

receiving a digital input signal with a predetermined clock frequency,

determining filter coefficients of a settable interpolation filter whoseamplitude response exhibits a lowpass-type attenuation curve in theuseful signal frequency band of the digital input signal,

filtering the digital input signal by means of the set interpolationfilter.

In the case of the method according to the invention, the filtercoefficients of the interpolation filter are preferably determined as afunction of a base function.

This base function is preferably stored in advance in a memory.

As an alternative to this, in accordance with a further embodiment ofthe method according to the invention the base function is generatedfrom prescribed fundamental functions.

In this case, a first fundamental function is preferably a time-limitedpower sine function.

The second fundamental function is preferably a first-ordersample-and-hold function.

In a particularly preferred embodiment of the method according to theinvention, a multiplicity of sets of filter coefficients of theinterpolation filter are generated as a function of the base functionwhich in each case exhibit in the useful signal frequency band anessentially identical amplitude response, but different group delays,there subsequently being selected for the purpose of determining thefilter coefficients of the interpolation filter that set of filtercoefficients whose group delay τ corresponds to the set desired groupdelay.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the interpolation filter according to theinvention for filtering a digital input signal, and of the methodaccording to the invention for digital interpolation of a digital inputsignal are described below with reference to the attached figures forexplaining features essential to the invention.

In the drawing:

FIG. 1 shows a typical circuit arrangement that contains theinterpolation filter according to the invention;

FIG. 2 shows a preferred embodiment of the interpolation filteraccording to the invention;

FIG. 3 a shows an amplitude response of the interpolation filteraccording to the invention;

FIG. 3 b shows the group delay of an interpolation filter according tothe invention;

FIG. 4 a shows the amplitude response of a first exemplary interpolationfilter in accordance with the invention;

FIG. 4 b shows the associated group delay curve of the interpolationfilter according to the invention with the amplitude response inaccordance with FIG. 4 a;

FIG. 5 a shows the amplitude response of a further interpolation filterin accordance with the invention;

FIG. 5 b shows the group delay curve of the interpolation filter withthe amplitude response illustrated in FIG. 5 a;

FIG. 6 shows an example of a base function that is used for determiningthe filter coefficients of the interpolation filter according to theinvention; and

FIG. 7 shows the curve of the group delay of a preferred embodiment ofthe interpolation filter according to the invention with the basefunction illustrated in FIG. 6, by comparison with the curve of thegroup delay of an interpolation filter according to the prior art.

FIG. 1 shows a typical circuit arrangement in which the interpolationfilter according to the invention is used to filter a digital inputsignal.

DETAILED DESCRIPTION OF THE INVENTION

An analog signal present on a line 1 is sampled by an analog-to-digitalconverter 2 with a sampling frequency f_(abtast), that is fed via aclock line 3, and a digitized output signal is output by theanalog-to-digital converter 2 to the interpolation filter 5 according tothe invention via a line 4. The interpolation filter 5 has setting lines6, 7 for setting the desired group delay τ and the dicimation factor K.The interpolation filter 5 filters the digital input signal present onthe line 4 and outputs a filtered digital output signal to a downstreamhighpass filter 9 via a signal line 8. The highpass filter 9 filters thefiltered output signal, present on the line 8, of the interpolationfilter 5 according to the invention once again and outputs acorresponding filtered output signal via a line 10.

The digital input signal present at the interpolation filter 5 has aclock frequency f_(in) that corresponds to the sampling frequencyf_(abtast) of the analog-to-digital converter 2. The filtered digitaloutput signal present on the signal output line 8 has an output clockfrequency f_(aus). The decimation factor K, which can be set via thesetting line 7, specifies the ratio between the input frequency f_(in)of the digital input signal and the output frequency f_(aus) of thefiltered digital output signal.

$\begin{matrix}{{K = \frac{f_{i\; n}}{f_{a\; u\; s}}}\;} & (1)\end{matrix}$

The interpolation filter 5 according to the invention has an amplituderesponse with a lowpass-type attenuation curve in the useful signalfrequency band of the digital input signal present on the line 4.Distortions in the digitized output signal of the interpolation filter 5occur because of the lowpass-type attenuation curve of the interpolationfilter. The downstream highpass filter 9 serves to remove thesedistortions that have occurred by compensating the lowpass-typeamplitude response of the interpolation filter 5 by means of anamplitude response that runs in a complementary fashion thereto.

FIG. 2 shows a preferred embodiment of the interpolation filter 5according to the invention illustrated in FIG. 1. The interpolationfilter 5 has a signal input 11 for receiving a digital input signal. Thedigital signal input 11 of the interpolation filter 5 is connected via aline 12 to a multiplier 13. The multiplier 13 multiples the digitalinput signal present on the line 12 by filter coefficients or weightingfactors that are present on a line 14 of the interpolation filter 5. Thefilter coefficients of the interpolation filter 5 are generated in thiscase in a filter coefficient generator 15 of the interpolation filter 5.The filter coefficient generator 15 is connected via internal settinglines 16, 17 to setting terminals 18, 19 of the interpolation filter 5.The desired decimation factor K can be set via the setting terminal 18of the interpolation filter 5. The desired group delay τ of theinterpolation filter 5 can be set at the setting terminal 19. The filtercoefficient generator 15 generates the filter coefficients as a functionof a base function. Here, in the embodiment illustrated in FIG. 2 thebase function is stored in a storage device 20 and is read out via aninternal line 21 by the filter coefficient generator 15.

In an alternative embodiment, the base function is not stored inadvance, but is generated by a base function generator as a function offundamental functions. The fundamental functions are preferably storedin a storage device in this case.

The digital input signal weighted by multiplication passes from themultiplier 13 via an internal line 22 to an accumulator 23 foraccumulating the weighted digital input signal. The accumulator 23includes an adder 24 that is connected on the output side to a register26 via a line 25. The output line 27 of the register 26 is fed back viaa line 28 to a second input of the adder 24. The output line 27 isconnected to a switching device 28. The switching device 28 can becontrolled via a control line 29 that is coupled to a resetting line 30for the register 26. The resetting line 30 is connected to a resettingterminal 31 of the interpolation filter 5. Furthermore, an internalresetting line 32 for the filter coefficient generator 15 is connectedto the resetting line 30. The switching device 28 is connected via aninternal line 33 to a digital signal output 34 of the interpolationfilter 5. The highpass filter 9 illustrated in FIG. 1 can, for example,be connected to the digital signal output 34.

The register 26 of the accumulator 23 can be reset via the resettingline 30, the accumulated digital value buffered in the register 26 beingoutput to the digital signal output 34 for reading out before theresetting via the switching device 28. The resetting terminal 31 of theinterpolation filter 5 is preferably connected to a central controller.

FIG. 3 a shows the amplitude response of the interpolation filter 5according to the invention. The amplitude response of the interpolationfilter 5 according to the invention has a lowpass-type attenuation curveas early as in the useful signal frequency band Δf_(nutz) of the digitalinput signal. The amplitude characteristic is slightly wavy in thehigher-frequency band and has a plurality of zero points. Theattenuation in this higher frequency band is very high. Theinterpolation filter 5 likewise has a certain attenuation, which must beconsciously accepted, in the useful signal frequency band ortransmission frequency band.

FIG. 3 b shows the associated group delay τ of the interpolation filter5. The group delay τ is the derivative of the phase response of theinterpolation filter 5 with respect to frequency. As may be seen fromFIG. 3 b, the group delay τ of the interpolation filter 5 in the usefulsignal frequency band Δf_(nutz) of the digital input signal isessentially constant and does not diverge until in higher-frequencyregions.

FIGS. 4 a, 4 b show the amplitude response and the associatedcharacteristic of the group delay τ as an example of an interpolationfilter 5 according to the invention having the following base functionBF(x):

$\begin{matrix}{{{BF}(x)} = {{{\sin( {t \cdot ( \frac{\pi}{12} )} )}^{12}{\sigma(t)}} - {( {{\sin( {t \cdot} )}\frac{\pi}{12}} )^{12} \cdot {\sigma( {t - 12} )}}}} & (2)\end{matrix}$

The filter coefficient generator 15 of the interpolation filter 5 usesthe stored or generated base functions to generate various sets offilter coefficients, each of which respectively has in the useful signalfrequency band Δf_(nutz) an essentially equal amplitude response butdifferent group delays τ. As may be seen from FIG. 4 a, the amplituderesponses that are generated by the various sets of filter coefficientsare essentially equal in the useful signal frequency band Δf_(nutz) upto f=0.45 f_(in). Here, f_(in) is the frequency of the digital inputsignal present at the digital data input 11 of the interpolation filter5.

As may be seen from FIG. 4 b, there are, however, differences betweenthe group delays, which are produced by the various sets of filtercoefficients that are generated by the filter coefficient generator 15on the basis of the base function. Inside the useful signal frequencyband Δf_(nutz), the group delays run in an essentially constant fashionin this case up to f=0.45 f_(in).

The filter coefficient generator 15 compares the group delays τ with thedesired group delay τ_(soll) set via the setting line 17, and selectsthat set of filter coefficients whose group delay corresponds inside theuseful signal frequency band Δf_(nutz) to the set desired group delay.That set of filter coefficients is selected in the case of which thedeviation between the group delay τ that is constant in the usefulsignal frequency band and the desired group delay τ_(soll) is minimal.

FIGS. 5 a, 5 b show a further example of an interpolation filter 5according to the invention whose useful signal frequency band isapproximately 0.24 f_(in). It may be seen from FIGS. 5 a, 5 b that theattenuation curve is of lowpass type inside and outside the usefulsignal frequency band.

FIG. 6 shows the characteristic of the base function BF(x) used, doingso for the interpolation filter illustrated in FIGS. 4 a, 4 b.

As already mentioned, a highpass filter 9 can be connected downstream ofthe interpolation filter 5 in order to compensate distortions producedby the lowpass-type attenuation curve of the amplitude response of theinterpolation filter 5. The series circuit of the interpolation filter 5with the highpass filter 9 preferably exhibits a sinc filtercharacteristic. Furthermore, a further interpolation filter ofconventional type can be connected upstream of the interpolation filter5 for the purpose of constricting the useful signal frequency band. Thisupstream interpolation filter can be a polyphase filter.

For the purpose of digital interpolation of the digital input signal,which has a specific clock frequency f_(in), the filter coefficients ofthe settable interpolation filter 5 are determined in such a way thatthe amplitude response exhibits a lowpass-type attenuation curve in theuseful signal frequency range Δf_(nutz) of the digital input signal. Thefilter coefficients of the interpolation filter 5 are determined in thiscase as a function of a base function BF. This base function BF iseither stored in advance in an internal memory 20 of the interpolationfilter 5, or generated by a base function generator on the basis ofprescribed fundamental functions BF.

Two fundamental functions are preferably used in this case, the firstfundamental function being a time-limited power sine function having thefollowing equation:h ₁(t)=sin [t·π/n] ^(m)·σ(t)−sin[t·π/n] ^(m)·σ(t−n)  (3)m,n>=1m, nεR,

σ (t−n) being the unit-step function at the instant n.

The second fundamental function is a first-order sample-and-holdfunction having the following equation:h ₂(t)=σ(t)−σ(t−n),  (4)σ (t−n) being the unit-step function at the instant n.

The base functions BF can either consist of the fundamental functions GFaccording to equation (3), (4) themselves, or be generated by logicoperations of the fundamental functions in the base function generator.

The logic operations comprise the following operations:

-   a) convolution of two pulse responses of the fundamental functions    in the time domain, and formation of a resulting new pulse response    as base function,-   b) shifting and multiplying the transfer functions in the frequency    domain, and forming a resulting new pulse response as base function,-   c) shifting and adding two equal pulse responses in the time domain,    and forming a resulting new pulse response as base function,-   d) adding two different pulse responses in the time domain, and    forming a resulting, new pulse response as base function,-   e) compressing and expanding, or expanding and compressing the pulse    responses in the time domain or frequency domain,-   f) raising the pulse response in the time domain to the power of a    rational number, and-   g) windowing the pulse response with the aid of a prescribed window.

If the calculation of the base function in real time is too expensive interms of circuitry, as an alternative to the generation of the basefunction it is possible for the base function to be stored as a sampledpulse response in a storage device 20, for example a ROM, of theinterpolation filter 5. In this case, the values stored in the basefunction memory 20 are read out by the filter coefficient generator 15.It is also possible for the pulse response of the base function BF to beapproximated by polynomials as a whole or in sections.

The base functions BF can also be generated by multiple logic operationson the basis of the fundamental functions GF.

The interpolation filter according to the invention meets variousrequirements.

The differences between the amplitude responses of the individualpolyphases are minimized for a prescribed outlay on circuitry.

The group delays τ of the individual polyphases continue to run in anessentially constant fashion inside a clock pulse period T_(in) of thedigital input signal.

Each individual polyphase has amplitude differences of at least 2 dB.

Furthermore, the interpolation filter according to the invention has alowpass characteristic.

It is also possible to construct hybrid systems with the aid of theinterpolation filter according to the invention. In this case, theinterpolation filter is split up into two polyphases, two architecturesbeing on offer for the implementation. Here, in the case of the firstarchitecture the even filter coefficients are multiplied by onepolyphase, and the odd filter coefficients are multiplied by the otherpolyphase. In the case of the other architecture, a lowpass signal isgenerated by adding the two polyphases. Thereupon, this signal isconvoluted with the sampled time-continuous filter. A high pass signalis likewise generated, by subtracting one polyphase from the other.Thereupon, each second sample is inverted in the case of thetime-continuous filter before carrying out signal convolution. Finally,the convoluted lowpass and high pass signals are added to one another.

FIG. 7 shows the group delay characteristic of an interpolation filter 5according to the invention by comparison with the group delaycharacteristic of a conventional interpolation filter according to theprior art, which exhibits a sinc filter characteristic.

In the example illustrated in FIG. 7, the interpolation filter 5according to the invention is an interpolation filter with 10 generatedfilter coefficients that each have a word length of 10 bits. In thiscase, the base function specified in equation (2) is used as basefunction for generating the filter coefficients. The interpolationfilter 5 according to the invention generates the group delaycharacteristic τ₁ which, as may be seen from FIG. 7, deviates onlyminimally from the set ideal group delay.

By comparison, the conventional interpolation filter generates a groupdelay characteristic τ₂ that deviates increasingly from the ideal or setgroup delay at higher frequencies. In the example illustrated in FIG. 7,the conventional interpolation filter, which has a group delaycharacteristic τ₂, is an interpolation filter with 256 filtercoefficients that each have a word length of 27 bits.

In the example illustrated in FIG. 7, because of the high number offilter coefficients and the large word length of the filtercoefficients, the conventional interpolation filter can be constructedonly with a very high outlay on circuitry that is far above the outlayon circuitry for the interpolation filter 5. As shown in FIG. 7, despitethe higher outlay on circuitry in the case of the conventionalinterpolation filter (5), the group delay characteristic τ₂ in the caseof the conventional interpolation filter 5 deviates substantially moresharply from the ideal desired group delay (τ_(ideal)) than does thegroup delay characteristic τ₁ in the case of the interpolation filteraccording to the invention.

List of reference numerals 1 Line 2 Analog-to-digital converter 3 Clocksignal line 4 Line 5 Interpolation filter 6 Setting line 7 Setting line8 Signal output line 9 Highpass filter 10 Line 11 Digital signal input12 Line 13 Multiplier 14 Line 15 Filter coefficient calculator 16Setting line 17 Setting line 18 Setting terminal 19 Setting terminal 20Storage device 21 Line 22 Line 23 Accumulator 24 Adder 25 Line 26Register 27 Line 28 Feedback line 29 Resetting line 30 Resetting line 31Resetting terminal 32 Resetting line 33 Output line 34 Output terminal

1. An interpolation filter for sampling frequency conversion of adigital input signal, the interpolation filter comprising: (a) a filtercoefficient generator for generating various sets of filter coefficientsas a function of a base function (BF), wherein the base function (BF) isgenerated on the basis of a time-limited power sine function h₁(t),wherein each of the various sets of filter coefficients has in a usefulsignal frequency band Δf_(nutz) of the digital input signal as anessentially equal amplitude response and different group delays τ,wherein the filter coefficient generator selects that filter coefficientset whose group delay τ has a minimal deviation from a set desired groupdelay; (b) a multiplier for multiplying the digital input signal by thefilter coefficients of the selected filter coefficient set; and (c) anaccumulator for accumulating the digital input signal weighted by themultiplication with the filter coefficients of the selected filtercoefficient set.
 2. The interpolation filter according to claim 1,wherein the base function (BF) is generated by a logic operation fromthe time-limited power sine function h₁(t) and a first order sample andhold function h₂(f).
 3. The interpolation filter as claimed in claim 1,wherein connected downstream of the interpolation filter is a highpassfilter for compensating the lowpass-type amplitude response.
 4. Theinterpolation filter as claimed in claim 3, wherein the interpolationfilter and the downstream highpass filter together exhibit a sine filtercharacteristic.
 5. The interpolation filter as claimed in claim 1,wherein the group delay τ of the interpolation filter runs isessentially constant in the useful signal frequency band Δf_(nutz). 6.The interpolation filter as claimed in claim 1, wherein the digitalinput signal is an equidistant digital signal with a predetermined clockpulse period T_(in).
 7. The interpolation filter as claimed in claim 1,wherein the group delay τ of the interpolation filter can be set insidea clock pulse period T_(in) of the digital input signal.
 8. Theinterpolation filter as claimed in claim 1, wherein the ratio of theclock pulse periods of the digital input signal T_(in) and the digitaloutput signal T_(aus) filtered by the interpolation filter can be set.9. The interpolation filter as claimed in claim 1, wherein a furtherinterpolation filter can be connected upstream of the interpolationfilter for the purpose of constricting the useful signal frequency bandΔf_(nutz).
 10. The interpolation filter as claimed in claim 9, whereinthe interpolation filter that can be connected upstream is a polyhasefilter.
 11. The interpolation filter as claimed in claim 1, wherein by astorage device is provided for storing the base function (BF).
 12. Theinterpolation filter as claimed in claim 1, wherein a controllableswitching device is provided for reading out the weighted digital inputsignal as a digital output signal.
 13. The interpolation filter asclaimed in claim 1, wherein the accumulator comprises an adder and aregister whose output is fed back to an input of the adder.
 14. A methodfor digital interpolation of a digital input signal, the methodcomprising: (a) receiving a digital input signal with a predeterminedclock frequency f_(in); (b) providing a base function (BF) on the basisof a time-limited power sine function h₁(t); (c) calculating varioussets of filter coefficients as a function on the base function (BF),wherein each of the various sets of filter coefficients comprises, in auseful signal frequency Δf_(nutz) of the digital input signal, anessentially equal amplitude response and different group delays τ; (d)selecting a filter coefficient set whose group delay τ has a minimaldeviation from a set desired group delay τ_(SOLL); (e) multiplying thedigital input signal by the filter coefficients of the selected filtercoefficient set; and (f) accumulating of the digital input signalweighted by the multiplication with the filter coefficients of theselected filter coefficient set.
 15. The method according to claim 14,comprising generating the base function (BF) by a logic operation fromthe time-limited power sine function h₁(t) and a first order samplefunction h₂(t).
 16. The method as claimed in one of claims 14 and 15,comprising storing the base function (BF) in a memory.
 17. The method asclaimed in claim 14, in which the time-limited power sine function h₁(t)function is as follows:h ₁(t)=sin [t·π/n] ^(m)·σ(t)−sin [t·π/n] ^(m)·σ(t−n) m, n>=1 m, n εR,σ(t−n) being the unit-step function at the instant n.
 18. The method asclaimed in claim 15, in which the first order sample function h₂(t)function is as follows:h ₂(t)=σ(t)−σ(t−n), σ(t−n) being the unit-step function at the instantn.